Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

TL;DR

This paper analyzes the energy gap behavior in a model of two coupled Bose-Einstein condensates, revealing how the gap varies with coupling strength and its impact on system dynamics.

Contribution

It provides analytical expressions for the energy gap minima and maxima and links these features to the system's dynamical behavior across different coupling regimes.

Findings

Energy gap is never zero when tunneling is non-zero.

A threshold coupling separates delocalized and self-trapping phases.

Minima and maxima in the energy gap influence the condensate dynamics.

Abstract

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunneling. The energy gap is never zero when the tunneling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalised phase from a self-trapping phase which occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Analytic expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.